WASHINGTON, Sept 12 (Reuters) - President Barack Obama onWednesday strongly condemned the killing of the U.S. ambassadorto Libya and three other embassy staff, calling it an"outrageous attack," and ordered stepped-up security at U.S.diplomatic posts worldwide.

The targeting of U.S. diplomats, in militant violencesparked by a U.S.-made film seen as insulting the ProphetMohammad, could raise questions about Obama's policy towardLibya in the post-Gaddafi era as he seeks re-election inNovember.

Obama, apparently seeking to seize the initiative in theaftermath of the attack, planned to speak to reporters in theWhite House Rose Garden at 10:35 a.m. EDT (1435 GMT) withSecretary of State Hillary Clinton at his side.

"I have directed my administration to provide all necessaryresources to support the security of our personnel in Libya andto increase security at our diplomatic posts around the globe,"Obama said in a written statement.

Ambassador Chris Stevens and three other U.S. diplomats werekilled as they rushed away from a consulate building inBenghazi, stormed by al Qaeda-linked gunmen blaming America forthe film that they said mocked the Prophet of Islam.

Sean Smith, a foreign service information managementofficer, was identified as one of the diplomats killed, in astatement by Clinton. The names of the two others were withheldwhile the government notified their families.

Stevens, a 21-year veteran of the foreign service, was oneof the first American officials on the ground in Benghazi duringthe uprising against former Libyan dictator Muammar Gaddafi lastyear.

Gaddafi was ousted by rebel forces backed by NATO air powerin August 2011 and was killed in October after months as afugitive.

Obama had hailed Libya's election in July as a milestone inits post-Gaddafi democratic transition and pledged the UnitedStates would act as a partner even as he cautioned that therewould still be difficult challenges ahead.

He had opted for a cautious strategy that steered clear of adominant role for the U.S. military and faced criticism fromRepublican opponents at home for what was described as "leadingfrom behind."

CAMPAIGN IMPACT

Before the full death toll and details of the Libya attackwere known, Obama's Republican presidential challenger, MittRomney, on Tuesday night criticized the Obama administration'sinitial response to violent attacks at U.S. diplomatic missionsin Libya as well as Egypt.

Pushing back hard, Obama campaign spokesman Ben LaBoltcriticized Romney for making a "political attack" at a time whenthe country was "confronting the tragic death of one of ourdiplomatic officers in Libya."

Obama was notified on Tuesday night that Stevens wasunaccounted for and was told on Wednesday morning of his death,a White House official said.

"I strongly condemn the outrageous attack on our diplomaticfacility in Benghazi, which took the lives of four Americans,including Ambassador Chris Stevens," Obama said.

"Right now, the American people have the families of thosewe lost in our thoughts and prayers. They exemplified America'scommitment to freedom, justice and partnership with nations andpeople around the globe and stand in stark contrast to those whocallously took their lives," he said.

Gunmen had attacked and set fire to the U.S. consulate inthe eastern city of Benghazi, the cradle of last year's uprisingagainst Muammar Gaddafi's 42-year rule, late on Tuesday eveningas another assault was mounted on the U.S. embassy in Cairo.

The California-born ambassador was trying to leave theconsulate building for a safer location as part of an evacuationwhen gunmen launched an intense attack, apparently forcingsecurity personnel to withdraw.

A Libyan official said the diplomats were killed when"gunmen fired rockets in their direction." White House and StateDepartment statements gave no details on exactly how the fourwere killed.

"While the United States rejects efforts to denigrate thereligious beliefs of others, we must all unequivocally opposethe kind of senseless violence that took the lives of thesepublic servants," Obama said.